ts] The Legendre polynomial LN is defined recursively by Lo(x) L₁(x) = 1 = Ꮖ LN(x) = 2N-1xLN-1(x)- LN-2(x) (N >1) Determine the polynomial Le explicitly by hand.

Q: Which of the following satisfies the statement f(x) is O(g(x)) when x5log(x+1) f(x) = +16x²? -5x3…

A: Given data:- fx=x5logx+1-5x3-2x33+16x2

Q: f (x) = (x + 2)(x - 1)[x - (4 + 3)][x - (4 - 3i)]

A: Given F(X)=(x+2)(x-1) [x-(4+3i)]]x-(4-3i]

Q: Use transformations of the graph of the greatest integer function, f(x) = int(x), to graph the…

A: g(x) = 3 int (x - 1)= 3f(x-1)  This means f(x) moves 1 unit right and stretched vertically by 3.

Q: For the function, f(x)= 1/2(1/2)x+3-6 determine: a)The transformations of the function on the…

A: a) Given that, Transformed function is f(x)=1212x+3-6 Parent function is f(x)=12x The parent…

Q: Suppose f(x) is a polynomial of degree 72. Can f(n)(0)=1 for all n>1. If it can give an example of…

A: Given that f(x) is a polynomial with degree 72.We have to see whether fn(0)=1 for all n≥1.

Q: Find the inverse function of the function f(x) = 2x5 on the domain x > 0.

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Q: write down the power seires for (x)(f(x))

A:

Q: If f (x) = –x² – 1, and g(x) = x + 5, then %D f(g(x)) = [ ? ]x²+[ ]x+ [ ]

A:

Q: Determine the characteristic polynomial of PA(T) = - A = 1 1 00 -4 0 -3 3

A:

Q: Let p be a polynomial of degree n and let  S = { x is an element in interval (0,pi/2) | cos(x) =…

A:

Q: Find a power function, f (x), such that the points (2, 9.6) and (5, 2343.75) lie on the graph of f…

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Q: Use calculus to show that if f(x) = (x − a)²g(x), where both f(x) and g(x) are polynomials, then…

A:

Q: Show that the product rule works for the case f (x) = x2, g (x) = x3.

A: Given that, fx=x2gx=x3 We have to show that the product rule works for the case of given functions.

Q: consider the functions f (x) =5/x and g(x)= x/x+2 A) evaluate and smiplify (f+g)(x) and state the…

A: fx=5x,  gx=xx+2 f+gx=fx+gx f+gx=5x+xx+2 f+gx=5x+2xx+2+x2xx+2 f+gx=5x+2+x2xx+2 f+gx=5x+10+x2xx+2…

Q: (c) Find all real values of x such that ln(2x+3)+ln(x − 2) = 2ln(x+4).

A:

Q: For each function g(x), describe the transformation from a base function of f(x) = x, f(x) = x²,…

A: The given functions,a) b) c) d) e) f) .We have to find the transformation of the function and then…

Q: (b) Find the multiplicative inverse of x + 1 + (x2 + 2x + 2) in Z3[x]/(x² + 2x + 2).

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Q: Determine the characteristic polynomial of PA(x) = | A = 1 -7 0 08 0 5 5

A:

Q: Use algebraic manipulation to prove that (x + y) · (x + ) = x

A: We need to prove that:Solving the Left Hand Side,Now, right Hand side,

Q: Find the composition m(n(x)), where m(x) = -8 and n(x) =- 11. %3D x+11 Based on your work above, do…

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Q: [cx)= (x+1) 「cx)-(x_)[cxー1) (xー1)「cx-1) [(-x)= [(1-x) |

A: Γ(x)=∫0∞tx-1e-tdt  for x>0Γ(x+1)=∫0∞txe-tdt =-txe-t0∞+x∫0∞tx-1e-tdt=xΓ(x)⇒Γ(x)=Γ(x+1)x Now,…

Q: Use transformations of the graph of the greatest integer function, f(x) = int(x), to graph the…

A: Greatest Integer Function:- The greatest integer function is a function that results in the integer…

Q: Find the composition f[g(x)] if: O 2-3u10 (10 - 15x2)5 O f(u) = u5 and g(x) = 2 - 3x² (2-3x²)²…

A: fu=u5 , gx=2-3x2